SOLUTION: An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the

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Question 149162: An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
By process of elimination and using random speeds and times, I have come up with the final answers of Express traveling at 50 mph and taking one hour to arrive in Chicago while the Local traveled at 25mph and arrived in Chicago in two hours. I cannot think how to express how to work this problem in algebraic terms - we are required to solve using linear equations. This problem is not in a textbook that I am aware of and I have been workin on this for 10 hours now. Please help....
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
an express and local train leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
:
The time they left is irrelevant to the problem
:
Let s = speed of the local
then
2s = speed of the express
:
Write a time equation: Time = dist%2Fspeed
:
Express time + 1 hr = Local time
50%2F%282s%29 + 1 = 50%2Fs
Get rid of the denominators, mult equation by 2s; results:
50 + 2s = 2(50)
2s = 100 - 50
2s = 50
s = 50%2F2
s = 25 mph speed of the local
then
50 mph speed of the express
;
;
Check solution
50%2F50 + 1 = 50%2F25
1 + 1 = 2